Ionizing radiation has been known as a carcinogen for a long time. But only about 40 years ago an epidemiological study was started with the survivors after the atomic bombing in Japan. Since then much data has been collected from this life span study (LSS) and from populations after exposures for medical indications. Cancer can be induced more or less in all tissues and organs by radiation. The radiosensitivity is different. High sensitivity is found in female breast, lung, bone marrow, stomach, colon and thyroidea. Leukemia can be observed five to ten years after exposures but other cancers occur only decades later. Infants, children and adolescents have a higher risk than adults. Measurements of risk have been possible after whole body exposures to high radiation doses (in the range > 100 mGy) and high dose rates. Risk estimates for lower doses are obtained by extrapolation under the assumptions of a linear dose response without a threshold. A dose of 10 mGy enhances the 'spontaneous' cancer rate by about .5%. The mentioned assumptions have to be proven by a better understanding of the mechanism of radiation-induced carcinogenesis. Around 3% of all cancers and 9% of leukemias are probably caused by exposures from natural sources.